An alternative solution method for dynamic analysis of axisymmetric shell problems

In this study, an alternative method for dynamic analysis of axisymmetric shell problems subjected to axisymmetric loading is theoretically investigated. The solutions of damped response of axisymmetric shells have been obtained by finite elements method in conjunction with Laplace transform method using the two dimensional plane elements. Materials of the shells are assumed to be isotropic, linear elastic and/or viscoelastic. In the viscoelastic material case, the Kelvin model is employed. According to the correspondence principle the material constants are replaced with their complex counterparts in the Laplace domain. The governing equations of motion of the problem are first obtained in the time domain. Laplace transform is then applied and the set of simultaneous linear algebraic equations are solved numerically in the Laplace domain. The solutions obtained are transformed to the time domain using the modified Durbin?s inverse numerical Laplace transform method. For the suggested model, a finite element analysis computer program is coded in Fortran. Verification of the program is performed by comparing the results of the present method with other numerical methods available in the literature. This procedure has proved to be highly accurate and efficient compared to various other numerical methods available in the literature.